Name
PHY107

### Does the size of the moon change more rapidly around a particular phase?

#### Exploration Phase

During December and January the length of the day is short and doesn't seem to change very fast. In early January the amount of daylight was increased about a minute a day. It slowly went to sunrise a minute earlier and sunset a minute later, or an increase of two minutes a day. In February it started to change more. Toward the end of February the day gained an average of two minutes in the morning and two minutes at night, for a total of four minutes a day. The amount of daylight gained was doubling. I started wondering how that worked. In December of 2011 the Washington Post had an article that explained this varying change in daylight hours.

With this exploration of the amount of daylight came other questions, but these concerned the moon. Did the phases of the moon do the same thing? Is the amount of moon that we see changing at a slower or faster rate around the time of the full moon? Does it change faster or slower around the new moon? What are the phases of the moon? How are they formed? Why don't we see the whole moon all of the time? Can the phase of the moon be predicted for a future date? Is information about the phases of the moon available for past dates?

For this investigation the question "Does the size of the moon change more rapidly around a particular phase?" was chosen.

#### Experimentation and Data Collection

The objective of the experiment was to determine if the amount of moon that is seen varies constantly or if it changes more rapidly at one time compared to another.

The first idea for an experiment was to observe the moon each night using a predetermined viewer that would be consistent from night to night. The shape of the moon could be drawn and scaled to the same scale each time and then the area shown could be calculated and the rate of change determined. In the end data was taken from MoonConnection.com where the phases of the moon are shown in a consistent manner over time.

Using the pictures at MoonConnection.com, the width across the middle of the moon was measured with a ruler for each day from the new moon in January to the new moon in February. The difference between each succeeding day was taken to see how the change in width varied with time. It is assumed that the change in width would be the same as the change in size.

Day Width (mm)+/- 0.5 mm Difference (mm) Day Width (mm)+/- 0.5 mm Difference (mm) 23 Jan 2012 0 New Moon 7 Feb 2012 11 0 24 Jan 2012 0.5 0.5 8 Feb 2012 11.25 0.25 Full Moon 25 Jan 2012 1.0 0.5 9 Feb 2012 11 0.25 26 Jan 2012 1.5 0.5 10 Feb 2012 11 0 27 Jan 2012 2 0.5 11 Feb 2012 10 1 28 Jan 2012 3 1 12 Feb 2012 9 1 29 Jan 2012 4 1 13 Feb 2012 8 1 30 Jan 2012 5 1 14 Feb 2012 6 2 31 Jan 2012 6 1 15 Feb 2012 5 1 1 Feb 2012 7 1 16 Feb 2012 4 1 2 Feb 2012 8 1 17 Feb 2012 3 1 3 Feb 2012 9 1 18 Feb 2012 2 1 4 Feb 2012 10 1 19 Feb 2012 1 1 5 Feb 2012 10.5 0.5 20 Feb 2012 0.75 0.25 6 Feb 2012 11 0.5 21 Feb 2012 0.5 0.25

### Change of Width (mm) vs. Moon Phases

 1.5 1.0 0.75 0.5 0.25 New Moon Waxing Crescent Full Moon Waning Crescent New Moon

It is assumed that the width of the visible moon across its center each day can be used to determine the change in size from day to day. The larger the change in size is, the faster the phases are changing.

#### Making Sense

Even though the data has some anomalies, at first glance it looks like the size of the visible moon changes most rapidly between the new moon and the full moon. It seems to change the least around the full moon. A prediction from this is that careful observation would show that the new moon is visible for a longer time than either the waxing or waning moon.

There is a lot of uncertainty with these numbers. It was difficult reading the ruler and those measurements are estimated to +/- 0.5 mm. Error bars could be drawn which would show the top of the error bars from the lower numbers reaching to the bottom of the error bars from the higher numbers. The overlap of error bars suggests that there isn't much difference in the data. So, upon further analysis of the data it appears that we have to say that the change in size is independent of the phase of the moon.

The small changes around the new moon could be due to the size of the moon at that time and would likely be even more pronounced if the actual size and not just the width across the middle was plotted. The bigger the size the less of a difference a small change would make. For instance, if the change in area is 0.1 mm2 and the area is 1.0 mm2, the change would be a big percentage of the total area. On the other hand, if the total area was 100 mm2 the change would only be a small fraction of the total area. This effect could also be different for the waning and waxing moon.

The sites that deal with moon phases have consistent pictures for the phases of the moon. See, for example, StarDate.org, MoonConnection.com, TuTiempo.net, etc.

The experiment could be improved by collecting the data from another site or from a printed page where the measurements could be done more accurately. The actual area of the moon could be measured. The tabulated raw data could suggest that it takes longer to go from the new moon to the full moon compared to going from the full moon to the new moon. It also suggests that the time just before the new moon is shorter than the time just after the new moon. New questions from this data could be:

1. Would more accurate data show a definite difference in the changes?
2. Is the change more rapid before the new moon compared to after the new moon?
3. Is the length of time different going from the new moon to the full moon compared to going from the full moon to the new moon?
4. Is it easier to measure the width when the moon is waning or when it is waxing?
5. Is there a better way to measure the size of the visible moon?